Which complex number has a distance of the square root of 17 from the origin on the complex plane?

Answers

Answer 1

Hey there! I'm happy to help! :D

-------------------------------------------------------------------

OVERVIEW

A complex number is a real number combined with an imaginary number (such as i, a number that will equal -1 when squared).

The complex plane is an interesting thing we use to graph complex numbers. The horizontal axis is where you plot the real part of the complex number, and the y-axis is where you plot the coefficient of the imaginary number.

For example, if I had the complex number 4+3i, I would plot the point (4,3) on the complex plane.

-------------------------------------------------------------------

MODULI

The modulus (plural is moduli) is the distance of a complex number from the origin on the complex plane. To find the modulus, you take the real number and the coefficient (basically the points of your graph), square them, add the results, and then you find the square root of that! Here's a little checklist so that you can always find the modulus of any complex number!

STEPS TO FIND MODULUS GIVEN COMPLEX NUMBER

STEP 1: PLOT THE COMPLEX NUMBER

Let's use our complex number 4+3i. If we plot it, the point will be (4,3)

STEP 2: TAKE YOUR VALUES OF X AND Y AND SQUARE THEM

4²=16

3²=9

STEP 3: ADD THESE SQUARES

16+9=25

STEP 4: SQUARE ROOT IT

√25=5

Therefore, the modulus (distance from the origin on the complex plane) of 4+3i is 5.

-------------------------------------------------------------------

SOLVING THE PROBLEM

In our case, we are given a modulus but not a point on the line. Our modulus is the square root of seventeen. We are going to have to the steps to find the modulus backwards to find our points. I will put the steps for finding a complex number given the modulus below.

STEPS TO FIND COMPLEX NUMBER GIVEN MODULUS

STEP 1: SQUARE THE MODULUS

√17²=17

STEP 2: FIND THE SQUARES THAT MAKE UP THE NUMBER

Before, we could just add things we found. Now, we have to find the things that were added! How do we know what things were added to find 17?  Well, we know that we added two squares to find the modulus, so we will subtract a square of some sort and hopefully come up with another square.

Let's see what squares exist that are less than seventeen.

1, 4, 9, 16

(Note that one is 1², 4 is 2², 9 is 3², and 16 is 4²)

Which of these can we add to get 17?

Well, we can do 1 and 16, so this is our result so far.

STEP 3: SQUARE ROOT THE RESULTS

Now, we just find the square roots of what we found in the last problem!

√1=1

√16=4

STEP 4: PLOT THE GIVEN NUMBERS ON THE PLANE AND FIND THE COMPLEX NUMBER

We can plot these either way because the modulus of 1+4i will be the same distance from the origin as 4+i because we only use the commutative property (adding order doesn't matter) when looking for the modulus. You can also have the negative version of either number because you immediately square it, so it can also be -4+i or 4-i! You can also rearrange the equation in tons of ways to figure it out. You could also have both be negative, flip the coefficient placement, etc.!

-------------------------------------------------------------------

SOLUTION

Therefore, the complex numbers that have a distance of √17 from the origin on the complex plane are ±4±i and ±1±4i. So, why did I write all of these funny plus and minus signs? Well, it's so that I didn't have to write all of the possible equations. I believe those equations actually represent 8 possible points we can create with the solution we got.

4+i

-4+i

4-i

-4-i

1+4i

-1+4i

1-4i

-1-4i

You can plug these complex numbers back in and find the modulus with my instructions to find the modulus given a complex number. Now, you will be able to deal with moduli and complex numbers for the rest of your life!

I hope that this helps! Have a wonderful day! :)


Related Questions

solve the equation for x and enter your answer in the box below
x + 14 =27

Answers

Answer: x = 13

Step-by-step explanation: When solving an equation like this, we are trying to get our variable which is our letter by itself.

So we first want to ask ourselves what is the 14 doing to x. Well, we can see that it's being added to x so to get x by itself, we will do the opposite of addition which is subtraction. So we subtract 14 from both sides of the equation.

The +14 -14 cancels out so we're left with x on the left.

On the right, we must subtract 14 from 27 to get 13.

So we have x = 13 which is the solution to this equation.

Answer:

[tex]x = 13[/tex]

Step-by-step explanation:

[tex]x + 14 = 27 \\ x = 27 - 14 \\ x = 13[/tex]

What is 13 - 4 x = 1 - x?

Answers

Answer:

x=4

Step-by-step explanation

Answer:

x = 4

Explanation:                                                                                                                  

Find the area of the parallelogram

Answers

Answer:

120 cm^2

Step-by-step explanation:

The area of the parallelogram is

A = bh

A = 15*8

A =120

Is Y=5x+2 in slope intercept form?

Answers

Answer: yes, the equation [tex]y = 5x +2[/tex] is a slope-intercept form.

Step-by-step explanation:

-The equation of a slope-intercept form:

[tex]y = mx + b[/tex]  (where [tex]m[/tex] represents the slope, and [tex]b[/tex] represents the y-intercept).

Yes the slope is is 5 and the y intercept is 2

Sarah is buying plants and soil for her garden! The soil Sarah wants costs $3.50 per bag, and the plants she wants are $8 each. Sarah can buy at most 20 items, as this is all she can fit in her car, and she cannot spend more than $150. Let x represents the number of bags of soil and y represents the number of plants:

Answers

Answer:

x+y ≤20

3.50 x +8 y ≤150

Step-by-step explanation:

Hi, the rest of the question is:

How do you write a system of linear inequalities to model the situation?

So, for the first inequality:

The sum of the number of soil bags (x) and plants(y) bought must be less or equal to 20.

x+y ≤20

For the second inequality:

The product of the number of soil bags (x) and the price of each bag (3.50) ; plus the number of plants bought(y) and the price of each plant (8) must be less or equal to 150.

3.50 x +8 y ≤150

In conclusion, the system is:

x+y ≤20

3.50 x +8 y ≤150

Which reason best describes why you can divide any number by 10 by moving the decimal point one place to the left?

1.Dividing a number by 10 is the same as subtracting the number ten times.

2. Dividing by 10 is the same as removing a zero.

3. Moving the decimal point left makes the number smaller.

4. Moving the decimal point one place to the left makes the number 1/10 of its original value.

Answers

4 is the answer

The next best is 3

Find the volume of a pyramid with a square base, where the area of the base is
8.7 m and the height of the pyramid is 10 m. Round your answer to the nearest
tenth of a cubic meter.

Answers

Answer: 29.0

Step-by-step explanation:

The volume of a pyramid is equal to l*w*h/ 3  and we know that the length times the width is the same as the base.

so we will multiply 8.7 * 10= 87 /3=  29

Volume = 87 m³

You need to multiply the area and the height to find the volume. If you have the length, width, and height, then you need to multiply and 3 and divide it by 3. Hope I helped :)

how do you write 2x - 2y = 8 in slope-intercept form ?

Answers

Answer:

y=x-4

Step-by-step explanation:

The general scaffold for the slope intercept form is y=mx+b, where m is the slope and b is the y intercept. You can rearrange the equation that you are given like this:

2x-2y=8

-2y=-2x+8

y=x-4

Hope this helps!

Answer:

Rearrange the equation so that it is written in slope intercept form:

y=mx+b.

2x+2y=8.

2y=−2x+8.

y=−x+4.

On Friday,2,364 cars parked in the garage at the mall. On Sunday 2,455 more cars parked In the garage than on Friday. How many cars parked in the garage during the two days?

Answers

Answer:

7183 cars

Step-by-step explanation:

On Friday, 2364 cars parked in the garage.

On Sunday, 2,455 more cars parked In the garage than on Friday.

This means that the number of cars parked on Sunday is 2455 plus the number of cars parked on Friday, that is:

2455 + 2364 = 4819 cars

Therefore, the number of cars parked in the garage in the two days is:

4819 + 2364 = 7183 cars

7183 cars were parked during the two days.

A square unit that is 1 unit wide and 1 unit long is a?

Answers

Answer:

A square with side length 1 unit, called 'a unit square,' is said to have 'one square unit' of area, and can be used to measure area.


Order each set of numbers from LEAST to GREATEST.

-4 , -5/4 , 0 , -5, -1.5

Answers

-5, -4, -1.5, -5/4, 0

Answer:

-5, -4, -1.5, (-5/4) -1.25, 0

Step-by-step explanation:

The higher the negative the lower the number (least).

~Anna

Need help? Contact me for tutoring!

What is the mean of the data set below? Round to the nearest tenth when necessary. 10, 30, 53 *

Answers

10+30+53=93 divided by 3 = 31 your answer is 31.

Isaiah was given a gift card for a coffee shop. Each morning, Isaiah uses the card to buy one cup of coffee. Each cup of coffee costs $2.50 and after buying 16 cups of coffee, the card had a $5 remaining balance. Write an equation for A(x),A(x), representing the amount money remaining on the card after buying xx cups of coffee.

Answers

Answer:

$45-$2.50xx

Step-by-step explanation:

Let first of all determine the original amount on the gift card as follows

amount utilized=$2.50*16=$40

balance left after utilizing $40=$5

original amount on the gift card=amount utilized+balance left=$40+$5=$45

if xx cups of coffee is purchased ,the amount utilized would be xx*$2.50

i.e $2.50xx

The equation for the amount left would total amount on the gift card minus the $2.50xx

equation for amount remaining =$45-$2.50xx

If the questioner has duplicated x,which means he or she meant just x

equation of the amount remaining would=$45-$2.50x

In the given figure, arcWY = 76° and arcXZ = 112°. What is the difference of the measures of angle WPY and angle XPY?

A. 8°

B. 9°

C. 16°

D. 18°

Answers

Answer:

C

Step-by-step explanation:

Answer:

A. 8

Step-by-step explanation:

#platolivesmatter

I NEED HELP WITH THIS

Answers

Answer:

(i think it is for q6 so) $6

Step-by-step explanation:

4.50÷3=1.50 (that's for 1 pound of fudge)

1.50×4=6

help meh
A timer rings every half hour for 3 1/2 hours.
Use your model to determine the number of rings.
dont make me feel like that was a waste

Answers

Answer:

7 times

Step-by-step explanation:

So since it rings every half hour, there should be 2 rings every hour, if not you are not on our planet. (60 mins in an hour, 30 mins = 1, so 60 mins =2)

So since it rings for 3 full hours, we get an initial step of 3 * 2 = 6 rings

Then there is another 1/2 ring because 3 and a 1/2 hours. So 6+1=7

hope i helped :) im not sure what you mean by model :(

Which expression represents finding the volume of the entire solid? Be careful

Answers

Answer:

Option 6

Step-by-step explanation:

To find the volume of a cone you use the formula 1/3*pi*r^2*h which would be pi*9^2*7. Then the volume of a cylinder is pi*9^2*50, so option 6 is right I believe.

21 radical sign p^-4/p^3

Answers

Answer: [tex]p^-^\frac{1}{3}[/tex]

[tex]\sqrt[21]{\frac{p^-^4}{p^3} }[/tex]

[tex]\sqrt[21]{p^-^4^-^3}[/tex]

[tex]\sqrt[21]{p^-^7}[/tex]

[tex]\sqrt[21]{\frac{1}{p^7}}[/tex]

[tex]\frac{\sqrt[21]{1} }{\sqrt[21]{p^7} }[/tex]

[tex]\frac{1}{p^\frac{7}{21} }=\frac{1}{p^\frac{1}{3} }=p^-^\frac{1}{3}[/tex]

Bryant collects a set of 20 values that represent the lengths of worms he found in the garden. The variance of the set of values is 36.

What is the standard deviation from the mean? Round the answer to the nearest tenth if necessary.

4.5
6
14
15.5

Answers

Answer:

The standard deviation from the mean is the square root of the variance.

Therefore, SD = sqrt(VAR) = sqrt(36) = 6

Hope this helps!

:)

:PROBLEM Bryant collects a set of 20 values that represent the lengths of worms he found in the garden. The variance of the set of values  is 36.

QUESTION. What is the standard deviation from the mean? Round the answer to the nearest tenth if necessary.

RESULUTIONS

4.5

6

14

15.5

ANSWER.=6

What is the Surface Area of the prism, in square centimeters?

Answers

Answer:

[tex]2( \frac{1}{2} \times 4 \times 6 ) + 2( 5 \times 10 ) + ( 6 \times 10 )[/tex]

[tex]= {184cm}^{2}[/tex]

i need the missing blanks .

Answers

Answer:

K, (-3.5,-5), E, (3.5, 3)

Step-by-step explanation:

you want to start a necklace making business. You spend $0.68 on string for each necklace and $0.25 on beads for each necklace. You sell your necklaces
for $2.00 each. If you sell 30 necklaces, how much profit will you make?

Answers

Answer:

Your profit would be 32.10$

Step-by-step explanation:

You spent 20.40$ on string, then you spent 7.50$ on beads too. That adds up to 27.90$ in total, so once you make your 30 necklaces you sell them for 2.00$ let's say you sell them all in one day your coming come with 32.10$ profit. Because you put 27.90$ into making the necklaces.

How can you determine if a point is a solution to a system of linear equations?
Please Help!

Answers

Answer:

You can substitute the x value of coordinate (x,y) in the equation. If the outcome = the y value in the coordinate (x,y), then you have determined it to be on the system of linear equations.

Step-by-step explanation:

Point P has a coordinates: ( Px , Py ).

You can choose which value is easy to substitute. Eighter start with the Py or you could start with the Px. It could save you time if you pick the right one for the job.

If you want to verify if any point is valid in any (linear) equation(s), you can:

a) substitute the x value of coordinate (x,y) in the equation, and if the outcome has the same value as y in the coordinate (x,y), then that point is a valid solution of the (linear) equation.

b) substitute the y value of coordinate (x,y) in the equation, and if the outcome has the same value as x in the coordinate (x,y), then that point is a valid solution of the (linear) equation.

Answer:

You can substitute the x value into the equation if the answer for y is the same for the y coordinate you will have your answer.

Step-by-step explanation:

these 15 colored pencils make up 20% of jordon's colored pencil collection.how many colored pencils does jordon have in his collections

Answers

Answer:

75 coloured pencils

Step-by-step explanation:

Let's say Jordon has x total pencils.

We know that 20% of these x pencils is 15, so we have:

20% * x = 15

Remember that % is just "out of 100", so 20% = 20/100 = 0.20. Then:

0.20x = 15

x = 15 / 0.20 = 75

Jordon has 75 coloured pencils.

Answer:

75 pencils

Step-by-step explanation:

Let the total no. of pencils be T

20% of T = 15

20/100 × T = 15

T = 15 × 100/20

T = 15 × 5

T = 75

What is the way to best choose the answers

Answers

The B option is the correct answer
I think opinion b is the correct answer if I am wrong please tell me

Write an equation for the line in slope-intercept form.

Answers

y = 1/2 x -3

Explanation: the y-intercept is where it crosses the y axis so the y-intercept is -3

50pts

Kadesha says that the triangles represent a translation. On a coordinate plane, triangle A B C has points (1, negative 1), (1, negative 4), (4, negative 4). Triangle A prime B prime C prime has points (1, 5), (1, 1), and (4, 1). Which explains whether Kadesha is correct?
A) Kadesha is correct because triangle ABC is the pre-image and triangle A prime B prime C prime is the image.
B) Kadesha is correct because each point in triangle ABC moves five units up.
C) Kadesha is not correct because the number of units between points A and B is different than those between points A primeand B prime.
D) Kadesha is not correct because a translation is a horizontal movement.

Answers

Answer: Option C is most Appropriate.

C) Kadesha is not correct because the number of units between points A and B is different than those between points A primeand B prime.

Step-by-step explanation:

Coordinates of vertices of ΔABC are =A(1,-1), B(1,-4),C(4,-4)

 Coordinates of vertices of ΔA'B'C' are =A'(1,5), B'(1,1),C(4,1)

Suppose, Preimage =ΔABC

Image =ΔA'B'C'

If you will find distance between two vertices of Both the triangles or length of sides of triangles

Kadesha is not correct because the number of units between points A and B is different than those between points A prime and B prime. Option (C) is the correct answer.

What is a graph?

"A graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner. The points on the graph often represent the relationship between two or more things".

For the given situation,

The triangle ABC has points A(1,-1), B(1,-4), C(4,-4)

The triangle A'B'C' has points A'(1,5), B'(1,1), C'(4,1)

Plot these two triangles in the graph as shown below.

The graph shows the relation between the triangle ABC and A'B'C'.

Both the triangles are separated by different units and are not images of one another.

Hence we can conclude that Kadesha is not correct because the number of units between points A and B is different than those between points A prime and B prime. Option (C) is the correct answer.

Learn more about graphs here

https://brainly.com/question/26657817

#SPJ2

Find the area of the shape shown below

Answers

The area of a trapezoid is A = (a+b/2)(h).
So just plug in your numbers.

determine whether the function represented by the equation is quadratic

Answers

Answer:

not quadratic because there is not a quadrat in it.

Step-by-step explanation:

The graph of a quadratic funtion is a parabola.

The general form of quadratic function is this:

f(x) = ax² + bx + c

Where a, b, and c are numbers.

Please uderstand that a can not be zero, which means that any quadratic function has at least one term with ² in it.

In this example, there is no quadrat visible, so it is not quadratic. By the way, y = -9x + 19 is a so called linear equation. It's graph is a line.

help please! ill mark brainliest

Answers

Answer:

A=150ft^2

Step-by-step explanation:

A=(b1+b2)/2*h

A=(15+10)/2*12

A=25/2*12

A=25*6

A=150ft^2

Area of trapezoid formula: A = h(b1+b2/2)

A = 12(10+15/2)

A = 12(25/2)

A = 12(12.5)

A = 150

Therefore, the area of the trapezoid is 150ft²

Best of Luck!

Other Questions
The difference of two supplementary angles is 70 degrees. Find the measures of the angles. What Is the Purpose of Education? The scores on one portion of a standardized test are approximately Normally distributed, N(572, 51). a. Use the 68-95-99.7 rule to estimate the range of scores that includes the middle 95% of these test scores. b. Use technology to estimate the range of scores that includes the middle 90% of these test scores. Which of the following is not a benefit of wildfires?A. Maintain forest clearingsB. Eliminate invasive plant species C. Allow some tree seeds to germinate D. Reduce leaf litter You walk in a room and on the bed there are 2 dogs, 4 cats, one giraffe, 5 cows and a duck, 3 chickens flying above; how many legs are on the floor? Which traits would Aristotle have used to classify sharks? Choose more than one answer. What is the affirmative command for Usted of SERVIR (to serve) Do you think that climate change has been presented to you as doom and gloom throughout your life? Explain. How does your heart rate affect the rate at which red blood cells travel throughout your body? PLEASE HELP ME QUICK!! The object below is a cubical lunch box having each edge as 10 cm.Find its surface area. A600 cm2 B360 cm2 C300 cm2 D36 cm2 Assume that Parker Company will receive SF200,000 in 360 days. Assume the following interest rates: the 360-day borrowing rate in U.S. is 7% while the 360-day borrowing rate in Switzerland is 5%. The 360-day deposit rate in U.S. is 5% while the 360-day deposit rate in Switzerland is 4%. Assume the forward rate of the Swiss franc is $0.50 and the spot rate of the Swiss franc is $0.48. If Parker Company uses a money market hedge, it will receive ____ in 360 days. A man wants to hike two trails. The length of one trail is 7.709 km. The length of the other trail is 9.0309 km. What is the total length of the two trails? Part B which details from the text best supports the answer to part a former red bow Crowl Corporation is investigating automating a process by purchasing a machine for $793,800 that would have a 9-year useful life and no salvage value. By automating the process, the company would save $133,000 per year in cash operating costs. The new machine would replace some old equipment that would be sold for scrap now, yielding $21,200. The annual depreciation on the new machine would be $88,200. The simple rate of return on the investment is closest to a. 5.80% b. 11.12% c. 16.72% d. 5.12% So they could get work, most of the immigrants settled:in the Westin large citiesin the Midweston the farms Which word from the expert creates parallel structure ? Someone help me pleaseeee Bonus Question3)According to the Supreme Court case, US v. Schenck, when are our First Amenchstent rights limited?A)When the press commits libel.B)When your freedom of speech causes chaos.When a petition has not been signed by enough people.DWhen your religion interferes with the public school system.One result of World War I was How did the invention of the Internet change people's daily lives?A. It allowed people to receive new media.B. It allowed people to avoid doing their choresC. It allowed people to stop paying taxesD. It allowed people to lose weight without exercising The box plots show the weights, in pounds, of the dogs in two different animal shelters.Weights of Dogs in Shelter A2 box plots. The number line goes from 6 to 30. For the weights of dogs in shelter A, the whiskers range from 8 to 30, and the box ranges from 17 to 28. A line divides the box at 21. For shelter B, the whiskers range from 10 to 18, and the box ranges from 16 to 20. A line divides the box at 18.Weights of Dogs in Shelter BOne-half of the dogs in each shelter are between which weights?between 8 and 30 pounds in shelter A; between 10 and 28 pounds in shelter Bbetween 8 and 17 pounds in shelter A; between 10 and 16 pounds in shelter Bbetween 21 and 30 pounds in shelter A; between 18 and 28 pounds in shelter Bbetween 28 and 30 pounds in shelter A; between 20 and 28 pounds in shelter B